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Mirrors > Home > ILE Home > Th. List > nfsbxyt | Unicode version |
Description: Closed form of nfsbxy 1818. (Contributed by Jim Kingdon, 9-May-2018.) |
Ref | Expression |
---|---|
nfsbxyt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-bndl 1399 | . 2 | |
2 | nfs1v 1815 | . . . . 5 | |
3 | drsb1 1680 | . . . . . 6 | |
4 | 3 | drnf2 1622 | . . . . 5 |
5 | 2, 4 | mpbii 136 | . . . 4 |
6 | 5 | a1d 22 | . . 3 |
7 | a16nf 1746 | . . . . 5 | |
8 | 7 | a1d 22 | . . . 4 |
9 | df-nf 1350 | . . . . . 6 | |
10 | 9 | albii 1359 | . . . . 5 |
11 | sb5 1767 | . . . . . . 7 | |
12 | nfa1 1434 | . . . . . . . . 9 | |
13 | nfa1 1434 | . . . . . . . . 9 | |
14 | 12, 13 | nfan 1457 | . . . . . . . 8 |
15 | sp 1401 | . . . . . . . . . 10 | |
16 | 15 | adantr 261 | . . . . . . . . 9 |
17 | sp 1401 | . . . . . . . . . 10 | |
18 | 17 | adantl 262 | . . . . . . . . 9 |
19 | 16, 18 | nfand 1460 | . . . . . . . 8 |
20 | 14, 19 | nfexd 1644 | . . . . . . 7 |
21 | 11, 20 | nfxfrd 1364 | . . . . . 6 |
22 | 21 | ex 108 | . . . . 5 |
23 | 10, 22 | sylbir 125 | . . . 4 |
24 | 8, 23 | jaoi 636 | . . 3 |
25 | 6, 24 | jaoi 636 | . 2 |
26 | 1, 25 | ax-mp 7 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wo 629 wal 1241 wnf 1349 wex 1381 wsb 1645 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 |
This theorem is referenced by: nfsbt 1850 |
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